What’s one and one and one and one

‘What’s one and one and one and one and one and one and one and one and one and one?’ Literature, Number and Death

A talk given at the 20th-2st Literature Seminar, University of Oxford, 4th December 2013. [pdf]

From Arnold onwards, literary-critical ideology has set itself against what Alain Badiou has called ‘the infinite excrescence of numbering’. If Leavis and Badiou are grotesquely at one in their loathing of ‘the will to submit the figure of communitarian bonds to number’ (Badiou 2008, 2), they are together at one with almost everybody else in sight in the humanities. Mathematics, of course, is made of and depends on number. But what if mathematics were opposed to number, so that mathematics and literature were in fact pulling at the same oar, in their efforts to mitigate the elementary horror, the slithy indifference of the White Queen’s ‘one and one and one and one’? And what if literary writing were also at times to be found, not recoiling from the death-in-life of number, but finding ways to put it to work? I will try to make out a few of the ways in which losing count is made to count in, say, Carroll, Dickens, Huxley or Beckett.

Shallowness

Mathematicians like to refer to certain problems of wide implication as ‘deep’. It is a quaint word, that is rarely heard in other areas, where it has a hint of unearned portentousness. But, of all areas of intellectual activity, mathematics is surely least of all to be characterised in this way. Numbers, the principal constituents of mathematics, are shallow – or, rather, they are absolutely without differentiation as regards their depth.

The curious thing about this flatness is that it is easily and universally apparent, yet almost everywhere resisted. Few people are actually able to bring to bear on numbers the equanimity they appear to enjoin. Most people have favourite numbers toward which they lean. Even if one is indifferent toward numbers, with no preference even for odd over even, the necessary prominence in our lives of certain numbers, the bus I take to work (91), my house-number at school (Middleton B 29), my employee number (355), my PIN, my date of birth, my invariant height and variable weight, seem to light up certain parts of the number line with significance.

Yet there is something unreadable about numbers, if by reading we mean an action of the mind that takes us from something manifest to something else that it indicates or implies, something in whose place it stands. The unreadability of numbers may be intimated by the word ‘decipher’, for a cipher was originally the name for zero, that number that is not quite one, that yields the name of the unreadability of numbers. Indecipherability seems to signify the particular kind of illegibility that attaches to numbers, that may endlessly be manipulated, but can never be penetrated.

If life seems to be a matter of qualities, themselves productive of and dependent on values, then numbers are death – the death of indifference or absolute equivalence. Though they may denote values, numbers do not have them, or they all have precisely the same value, the value of marking some quantity. Qualities are not interchangeable, though they are linked together by relations. Numbers are their relation and nothing more. You may, as Richard Rorty observes, define a number like 17 in an infinite number of ways – but you will never be able to do any more than this.

Numbers do not have values, because they are the measure of them. Titian’s Diana and Actaeon is worth £50 million – but what is ‘50 million’ worth? The value of something is that to which it is equivalent, something else into which it may be translated or for which, under certain circumstances, it might be exchanged. For a moment, this might indeed look like a kind of mathematical operation. Verily, the value of 17 is expressible as the ‘something else’ of 12+5 or 11+6. But there really is no else or other in this case, as there is in the case of the price attached to a Titian painting, and for what seems for a moment to be a surprising reason. A Titian can be worth £50 million precisely because a Titian is not £50 million pounds, precisely because it can never be fully exchangeable with it. To be sure, I can purchase the Titian for £50 million, but that exchange is not the same as full equivalence, for the previous owner of the Titian cannot treat the £50 million cheque in the same way as the Titian (and if he could the situation would be absurd, it would amount to exchanging a Titian for another Titian that was identical in every conceivable way, or exchanging it for itself). So there can be exchange only where there is not identity. But this is not the case with the 12+5 or 11+6 and so on that constitute 17, precisely because they constitute it. 17 is not worth 12+5, because it is nothing other than the fact of its being 12+5. The alternative expressions for 17 are precisely its identity, not something that stands in place of that identity. Here, in other words, one really does exchange something for itself, and precisely because it is nothing other than the fact of this exchangeability, and the sum total of all the possible exchanges that will add up to, or subtract down to it.

What is more, there is absolutely no reason to prefer any of these ways of making up 17 to any other. Any one will do just as well as any other for the job of defining 17. This might seem odd in the case of 17, in particular, the 7th prime you get to when you count from 2 upwards. To discover that 17 is a prime is to discover another kind of equivalence for it than the 1+16 and the 2+15 kind, and the prestige of primes makes it seem as though this is a more important and essential thing about 17 than the numbers of which it is made. But it is really not – it is just another form of that equivalence to other numbers that define all numbers.

17 happens to be my favourite number. It happens to be that 17 is one of only 5 known Fermat primes. A Fermat number is a number such that Fn = 2(2n) + 1; 17 is the Fermat number derived from 2. But though these are properties that seem to render it unique, this is not to say any more than that we can pick it out for attention in certain ways, and this is equivalently true for all numbers. Because all numbers are definable in an infinite number of ways, the things that seem to make certain numbers special are just selections from that infinite number of ways. It may seem impressive and mysterious that certain numbers seem to have rare or unique properties, but in fact every number has at least one absolutely unique property – in that it comes between two other numbers in the counting continuum. Every number is generically unique, which means that no number is unique in being unique. Uniqueness is what makes numbers so monotonously uniform, not what rescues tham from that uniformity.

Picking out certain numbers for special attention is the traditional way of redeeming numbers for human life, because it skews and bunches a system of absolute equivalence into one of differential values, creating a lumpy, striated landscape out of one that is otherwise smoothly uniform. Magic numbers, or lucky numbers, suggest that, far from being homogenous and indifferent, certain numbers do in fact have special qualities or powers – the rule of three, the seventh son of a seventh son, unlucky 13 and so on. The study of numbers in literature has often depended on this kind of numerological magic.

This book proposes, by contrast, that it is precisely as the principle of differentiated indifference (numbers are all different from each other in exactly the same ways) that numbers might have the force they do in literature. And this is the reason that this is a book about numbers and writing, rather than about mathematics and writing. For number is the matter rather than the form of mathematics. Numbers are what mathematics works on, what it is necessary to be in order for mathematical operations to take place. This is perhaps the reason why a purely mathematical definition of number may have been so hard to derive. Because mathematics thinks with numbers, because it is, precisely, numerical thinking, it has been hard for mathematics, on its own, to think about number.

In this sense, although mathematics is made of number, and works in and through it, it is fundamentally opposed to it, precisely because it is the redemption of number. Mathematics, and especially that branch of it known as number theory, shows that numbers are not just numbers – that they are tied together by hidden webs of relationship and entailment. By being mathematical, we learn to overlook the most important and defining features of number, namely the flat indifference of numbers.

It is this feature of number which the Red Queen discloses:

‘Can you do Addition?’ the White Queen asked. ‘’What’s one and one and one and one and one and one and one and one and one and one?’

‘I don’t know,’ said Alice. ‘I lost count.’

‘She can’t do Addition,’ the Red Queen interrupted.

‘Doing addition’ means being able to process a stream of identical ones into consecutive products, using the embodied adding machine known as counting. This simple action, which seems elementary, is in fact a way of providing orientation, or converting the shallowness of number into a kind of depth. Counting is a way of not ‘losing count’ amid the swirl of pure numbers.

A number is nothing more than the sum total, the unsummable total, of all its relations to all the other numbers there might be. For any number, there is no number to which it will not have some relation, and no relation to any number that is more important or intrinsic than any other. One cannot say that it is more important that seventeen is three added to fourteen than that it is eighty-two subtracted from a hundred. Of course, one may well be more interested in certain relations than in others – in the fact, for example, that seventeen is divisible only by one and itself, that is, that it is a prime number. But all numbers have particular properties of this kind.

To be a living entity is to have some kind of here and now, to occupy some particular portion of time and space that can never be merely equivalent to some other portion of time and space. What we call life is perhaps no more or less than this quality of thisness, or itselfness. It is this thisness that number disperses, flattening it out into equivalence. Number gives control, because number requires and supplies distinctness, the possibility of series and finitude (distinguishability and countability). But it does so at the cost of the sense of what is called the qualitative, which is to say the drastically asymmetrical, nonreversible world in which my meaning and value is never simply commutable into yours or hers. This absolute equivalence is what I will call death: death, not as nonbeing, but as absolute equivalence, the absence of any difference that would make a difference between one mode of being and another.

The horror of number is that any and every number can be counted out as a succession of ones, added to each other (including, of course decimals and fractions. The units that make up a number are absolutely interchangeable; no one differs in any respect from any other one. And yet those ones are not the same, because they can be added to each other. Counting is a matter of one, then another one, exactly the same, and another one. It is a horror, because it is a vision of indifference – of an absolute differentiation, which makes, or is founded on no difference at all, with the number line being a distension of identicality. Indeed, there is evidence that we will not allow ourselves to believe what we claim to know, namely, that the one that is added to eleven to make twelve is the same as the one added to two to make three. Because it is somehow further away, it seems to many that it must be smaller, because distant objects appear smaller than proximate ones.

Mathematics are less at home in this world than those who think of themselves as unmathematical. Their effort is to generate quality from this grey, toiling mortar of indifference, to build from it a variegated landscape, of pattern, recurrence, contour. And most of all to avoid counting. Solutions that rely on the simple counting out or counting up of possibilities are known by mathematicians as ‘brute force solutions’, because they do not involve any calculation. There is mathematics in the head of the sunflower because it has discovered, or rather is itself the stochastic precipitate of the discovery, that the most efficient way to pack seeds in a given space is to coil them in a spiral at intervals of .618 of a complete rotation, the golden section, or the ratio between successive numbers in the Fibonacci sequence. But the mathematics of the sunflower is immanent to it, not something it can do. Because it is the performance it cannot itself perform that performance. So counting seems unmathematical, because it seems closer to the mathematics that we are than the mathematics we do – hence, perhaps, brutish, natura naturans rather than natura naturata. Perhaps one answer to the White Queen’s question is ‘me’, the one that never comes out as one.

Counting is at the heart of mathematical procedure, because every mathematical procedure amounts to, or can come down to counting. (Whenever one uses an expression like ‘every x’, one is saying that, if one were to count out all the procedures in question, there would be none left over). And yet mathematics and counting are inimical to each other. We learn to count, which is to say, we train ourselves into a kind of automatism. Counting is never something we can exactly do, precisely because we have in it to give ourselves over to a doing that does itself. The ambivalence of this is noted in Elizabeth Sewell’s The Field of Nonsense. She argues that

The Nonsense writer wants to make a world out of language and the mind’s pattern of reality, but reality which will be remade so as to be more subject to number; and the characteristics of number and order will have to be imparted to the images in the mind so that they too may be controlled, distinguishable from one another, going along one at a time in an ordered series, limited and exact.

The use of numbers allows for this control because perceptions ‘will be brought under stricter control than is usual in language, and in this state they could be played with’ (Sewell 1962, 65). But number involves two associated principles, that of distinctness of units, and that of seriality. Sewell associates them, but there are occasional hints that they may pull in opposite directions, as when she writes that ‘as the mention of any number must do, it sets the mind running along the familiar and ordered series of natural numbers. The mind by the very mention of number is delivered into the hands of its own ordering tendency’ (Sewell 1962, 67, my emphasis). There is surely no need for me to spell out at length the implications of this ambivalence, which is of course just why I propose to do so, since unnecessariness is sitting right in the middle of these considerations. In Nonsense, the mind is given the freedom to play by a formalization that makes it more the master of the world; but this kind of play also means that one is at a certain risk of being played with the ordering tendency that is essential to the impulse to play. Life expresses itself most fully in play, in which death is inevitably recruited.

We can extend this far beyond the writing of Nonsense. The horror of counting is that there is no end to it. Compulsive counters aim to make the world controllable by reducing it to number, by making it enumerable. But compulsive counters find themselves compelled by the force of compulsion they attempt to exercise upon the world. Counting means adding one to one to one to one. One adds one, then adds another one, then another. But what is one of something? One is the quality of being one that any one thing has in common with another thing that can be counted as one. One must be able to count two things as one for either one of them to count as one. In counting, one is never a complete unit, for one must be added to it, then another one. Unless there could be another one to be added to any one, it would remain less than one, come up short of the one that it must nevertheless be taken to be in order for counting to ensue. You must just assume you know what one is in order to add another one to it, even though only that addition will confirm the oneness of the one. If there really were only the One, if there were no real division in the universe, then that universe would not yet be thinkable as a one, for it would not be possible to step outside it to count to two. One must always be more than one in order to avoid being less than one. One is always a more-than-one that is less than one, for counting will never let you get the one to add up exactly to itself.

John Perceval, the son of the assassinated prime minister Spencer Perceval, published an account of his delusions during the period of madness into which he fell in the 1830s, and which led to him being incarcerated in a number of asylums. Among the milder delusions he records is of an internal counting mechanism that overtook him when he was trying to get to sleep:

Weary at length, and unable to comprehend these commands, I sought for sleep, and recollecting what my mother had formerly [304-5] told me of my father, that he used when he found himself unable to obtain rest, to keep continually counting to himself, I tried the same. But then the power of thinking numbers for myself was taken from me, and my mind or life lay in my body, like a being in a house unable to do anything but listen to the sound of others talking around him, and voices like the voices of females or fairies – very beautiful – very small, and with a rapidity I cannot describe, began counting in me, and entirely without my control. First, one voice came and counted one, two, three, four, up to ten or twenty – then a second voice took up the word twenty, and kept repeating twenty – twenty – twenty – whilst another after each twenty called one – two –three – four, and so on till they came to thirty – then another voice took up the word thirty, and continued crying thirty – thirty – thirty, whilst a voice called out after each thirty – one – two –three – four, and so on till they came to forty, and thus the voices within me proceeded, dividing the labour between them, and so quickly, that I could not possibly pronounce the numbers.

I conceive from this and other experiences that the mind acts by beautiful and delicate machinery, which is disorganised in all men by sin and violence – by perverseness. (Perceval 1840, 304-5)

Problems that can only be solved by brute force, such as the varieties of the TSP, or travelling salesman problem, which involves finding the shortest itinerary between any sequence of points that will involve visiting each point once and only once, are regarded as mathematically insoluble. The fact that ant colonies are able to solve this problem by trial and error, and that artificial ant colonies may be generated to do it, does not make the solutions any more mathematical, because they are all blind, and it is this blindness that accounts for the horror of merely counting. Mathematics comes into being as a recoil from this horror.

Horror, because horror is at its heartless heart uncountability. Freud suggests that the head of the Medusa signifies castration, not just because it is decapitated, but also in ‘confirmation of the technical rule according to which a multiplication of penis symbols signifies castration’. No mention of this ‘technical rule’ appears to my knowledge anywhere else in Freud, which suggests a nonce-rule, or a once-rule, a rule which is more-than-one (as all rules have to be), yet also less-than-one (since it is a rule applied only for this occasion, like Rule Forty-Seven in Alice’s court). Norman O. Brown remarks that, in this world where the many can stand both for the less than one and the more than one that protects against it, ‘We are in a world oscillating between the one and the many, a world of fission and fusion, the world of schizophrenia; the world of the schizophrenic patient whose “primary function in life, as he saw it, was to restore people who had been multilated” ‘ (Brown 1966, 66, quoting Géza Róheim) Horror refers to the sensation of bristling, in which the skin, that organic avatar of the integer, may lose its integrity, standing up as though multiplied into hairs, or shivering, shuddering, or quaking. Horror is dispersal amid multiplicity, a dissolution into the innumerable. Horror is simply losing count.

Counting up and counting out are defences against this horror of indifference, but they also threaten to expose us to it. Counting exposes us to the one-by-one of every composition, the material substrate of every relation. Counting exposes us to the very dread of losing count from which it preserves us. Noel Carroll’s Philosophy of Horror suggests that horror is a reaction to forms of indistinctness, or fusion. It might seems as though the horror of number contradicts this, since number is the very principle of distinctness. But there is a special horror in the indistinctness that results from the pseudo-distinctiveness of number. A quantity is definite and absolute, it may seem to have an aura or quality about it. But it is made up of the joining of a certain number of indistinct units, indistinct because they have to be accumulations of the absolutely identical, of an entity added inexorably to itself. There can be little doubt that the horror of insects has to do with their multiplicity, with the sense of unbearable, spawning multitude they provoke – if they crawl over us, they induce the sensation of our skin itself, as we say, crawling. The categorial uncertainty of the spider has something to do with the fact that we are not sure how many legs it has (eight is close to the limit of our subitistic power to grasp a number without needing to count it). Knowing that it has eight and not six is a sort of protection against the sheer uncountability of its legs. Added to this is the horror that the fly or spider seems indifferent to the subtraction of one or more of its legs. So spiders and flies embody the horror of number because they seem so indifferent to the very numbers that differentiate them. Numbering is a superstitious protection against number. No millipede has a thousand legs, though some have as many as 750. It is possible for a centipede to have a hundred legs, but for a reason that, for some reason, I find truly appalling, namely that centipedes always have an odd number of pairs of legs.

Counting belongs to both sides of number, to the formed and the formless, the discontinuous and the endlessly ongoing. When the victim of a flogging is required to call out the number of lashes inflicted upon them, they are being invited on to the sadist’s side, and offered the chance of maintaining a kind of syntax of pain, even as the very requirement to exercise that self-mastery increases the demand and the potential penalty of losing count. But counting always exposes one to the chance of losing count. We teach children to count to protect them against the horror, claustrophobic and agoraphobic at once, of the one and one and one and one of the countless or uncountable.

Modernist writers of course mount a sustained assault against the realm of number, determined to assert quality over quantity, determined to assert the hazy, nebular, indefinite or indistinct, which is said to be living, over the exact and numerable world, which is said to be abstract, mechanical, and dead, or male for short. Of course, there is also to be found, in the words of a Birkin in Women in Love, for example, an aristocratic ideology of the absolutely nonrelativity of value:

‘We’re all the same in point of number. But spiritually, there is pure difference and neither equality nor inequality counts. It is upon these two bits of knowledge that you must found a state. Your democracy is an absolute lie—your brotherhood of man is a pure falsity, if you apply it further than the mathematical abstraction.’

Lawrence’s writing, so relentlessly pitted against number, is in fact more strangely mesmerised by it than almost any other modern writer (I have a feeling that there is a higher number of number-words to be found in his work, especially big number words, like hundreds, thousands and millions, than in most other modern writers.) There is, for example, Gudrun, thinking about Gerald’s mechanism:

The wheel-barrow – the one humble wheel – the unit of the firm. Then the cart, with two wheels; then the truck, with four; then the donkey-engine, with eight, then the winding-engine, with sixteen, and so on, till it came to the miner, with a thousand wheels, and then the electrician, with three thousand, and the underground manager, with twenty thousand, and the general manager with a hundred thousand little wheels working away to complete his make-up, and then Gerald, with a million wheels and cogs and axles.

Poor Gerald, such a lot of little wheels to his make-up! He was more intricate than a chronometer-watch. But oh heavens, what weariness! What weariness, God above! A chronometer-watch—a beetle—her soul fainted with utter ennui, from the thought. So many wheels to count and consider and calculate! Enough, enough—there was an end to man’s capacity for complications, even. Or perhaps there was no end.

Two antagonistic principles are locked together here, as they perhaps are in every articulation of the ideology of number. The first is the idea of Gerald’s mechanism, which consists in reducing life to distinct and countable units. This produces order, control, predictability. But this very exactness produces the intolerable indistinctness of the indifferently non-identical, the ‘madness of dead mechanical monotony and meaninglessness’. In its account of Gudrun’s meditations, Lawrence’s narration becomes a kind of counting-up procedure, going up in squares, 1, 2, 4, 16, but precisely in order to be able to open on to the uncountable ‘so on’, the losing count that lurks in every counting procedure. This is the basis of Brian Rotman’s arguments against infinity in Ad Infinitum (1993); the number line cannot in fact go on infinitely, because there must inevitably come a point where the informational resources required simply to set out one number and then add one to it would exceed the computational power available in the universe. There would have to come a point in counting up where the universe would have to lose count.

What is there to set against this? There are the various forms of intensity, the modernist moments of being, the radiant epiphanies, the incommensurable ‘events’. In Women in Love, there is Mrs Crich, who ‘lost more and more count of the world, she seemed rapt in some glittering abstraction, almost purely unconscious’ – though ‘she bore many children’. And there is Hermione, in her consuming fantasy of murdering Birkin:

A terrible voluptuous thrill ran down her arms—she was going to know her voluptuous consummation. Her arms quivered and were strong, immeasurably and irresistibly strong. What delight, what delight in strength, what delirium of pleasure! She was going to have her consummation of voluptuous ecstasy at last. It was coming! In utmost terror and agony, she knew it was upon her now, in extremity of bliss. Her hand closed on a blue, beautiful ball of lapis lazuli that stood on her desk for a paper-weight. She rolled it round in her hand as she rose silently. Her heart was a pure flame in her breast, she was purely unconscious in ecstasy. She moved towards him and stood behind him for a moment in ecstasy. He, closed within the spell, remained motionless and unconscious….Then swiftly, in a flame that drenched down her body like fluid lightning and gave her a perfect, unutterable consummation, unutterable satisfaction, she brought down the ball of jewel stone with all her force, crash on his head. But her fingers were in the way and deadened the blow. Nevertheless, down went his head on the table on which his book lay, the stone slid aside and over his ear, it was one convulsion of pure bliss for her, lit up by the crushed pain of her fingers. But it was not somehow complete. She lifted her arm high to aim once more, straight down on the head that lay dazed on the table. She must smash it, it must be smashed before her ecstasy was consummated, fulfilled for ever. A thousand lives, a thousand deaths mattered nothing now, only the fulfilment of this perfect ecstasy.

But this principle derives from and depends upon the rounding-up or counting-as-one of the idea of the ‘mathematical’ or the ‘mechanical’. Moments of intensity must be rescued from the nightmare of monotonous numbering, but the logic that does the rescuing must nevertheless be numerical, in that it must assert itself as a transcendent one, now conceived as an absolute, and entirely impossible equality to itself. It is a transcendent counting-as-one of that which transcends counting altogether, but is really an apotheosis of the number one, as though there could be a one that bore no relation to any other kind of singularity. But a singularity that bore no relation to any other singularity would not be anything. Lawrence retreats from numerical horror, in which the ones can never be got to add up into a nameable, numerable total, into numerical fantasy, the idea of a one that must always hover asymptotically below the threshold of the dead consummation of being a one comparable to any other one (the horror of democracy). There is an erosion of the one at either end of the scale, the elementary and the ultimate. Numeration is the deterrence of this erosion, this failure of the one to stand up and be counted. Ecstasy, the event, are the singular without seriality, a consummation that can never be summed up, a uniqueness that goes beyond or refuses to be cashed in as the merely unitary, which is the nullity of the one-like-another-one.

In fact, Lawrence is obsessed with number, and enraged at its capacity of number to resist numeration, its capacity to make us lose count. He declares in ‘Bestwood’ ‘What we should strive for is life and the beauty of aliveness, imagination, awareness, and contact. To be perfectly alive is to be immortal.’ (Lawrence 1970, 266). Lawrence sees quantity as death itself – but acting on the impulse to preserve life against death actually requires the most brutal entry into the quantitative, in the form of culling: ‘I know that we should look after the quality of life, not the quantity. Hopeless life should be put to sleep, the idiots and the hopeless sick and the true criminal. And the birth-rate should be controlled’ (Lawrence 1970, 266).

Beckett’s characters are addicted to counting, but also liable to lose count; indeed the latter is probably the reason for, and consequence of, the former. As for example at the beginning of ‘The Expelled’:

There were not many steps. I had counted them a thousand times, both going up and coming down, but the figure has gone from my mind. I have never known whether you should say one with your foot on the sidewalk, two with the following foot on the first step, and so on, or whether the sidewalk shouldn’t count. At the top of the steps I fell foul of the same dilemma. In the other direction, I mean from top to bottom, it was the same, the word is not too strong. I did not know where to begin nor where to end, that’s the truth of the matter. I arrived therefore at three totally different figures, without ever knowing which of them was right. And when I say that the figure has gone from my mind, I mean that none of the three figures is with me any more, in my mind. It is true that if I were to find, in my mind, where it is certainly to be found, one of these figures, I would find it and it alone, without being able to deduce from it the other two. And even were I to recover two, I would not know the third. No, I would have to find all three, in my mind, in order to know all three. Memories are killing. So you must not think of certain things, of those that are dear to you, or rather you must think of them, for if you don’t there is the danger of finding them, in your mind, little by little. That is to say, you must think of them a good while, every day several times a day, until they sink forever in the mud. That’s an order.

The work in which Beckett comes closest to immersing himself and his reader in the destructive element of number is surely Watt and, within that novel of obsessive accumulations, permutations and calculations, the most sustained exercise in mathematised narrative is the episode, allegedly recounted by Arthur to Watt and others in Mr Knott’s garden, which deals with the appearance before a College committee of Ernest Louit, accompanied by what he claims to be a mathematical savant from the far West of Ireland, in order to account for the £50 of college funds that he has expended in research for the dissertation he entitles The Mathematical Intuitions of the Visicelts.

Conclusion

The ideology of number in the modern world is that number is inhumanly exact, while the realm of the word, the tone, the gesture, is vitally imprecise. We are many of us still spontaneous Bergsonians in this respect, favouring the fuzzy continuities of the temporal against the harsh, anonymous, mechanical, severing pseudo-exactness of the spatial. The phrase ‘the exact sciences’ sums up (hah!) the difference between the realms of the inhuman mathematical and the human. But the mathematical is not the realm of number. The exposure to pure number, or pure exposure to number exacts a kind of horror or delirium, which does not belong to either side of the exact/inexact equation, precisely because it is not equal to anything, not even itself.

Literary writing will often incorporate the idea of number as exactness, in order to immunise itself against it, in order to keep the equation balanced between the mathematical-mechanical and the unmathematical organic, in order to assert its powers of life over the deathliness of number. But the deathliness of number is also a strange life-in-death. Freud’s account of the way in which the death instinct routes itself through life is a dramatisation of this. Death wishes to be the zero that answers and balances the one that is life. But in order to do this, life must be made to add up to one – death that supervened upon a life that was not yet a life would not be death. So death must put itself off, must start a count through life that will never come to an end, since being alive means losing count. To die exactly is impossible, because there are too many things to be ‘lived off’ as Freud weirdly, brilliantly puts it, of which account would have to be taken. The failure to be one, the certainty of losing count in the more-than-one that will always be less-than-one, is what puts number, the very domain of the deathly, on the side of life, as the indefinite, as the not-yet-finished, the ‘giant tot’ of the ‘unnullable least’ as Beckett puts it, that can never be reached. Number is the secret, craving delirium at the heart of writing precisely because writing must set itself against the fantasy of number as exact.

To be a living entity is to have some kind of here and now, to occupy some particular portion of time and space that can never be merely equivalent to some other portion of time and space. What we call life is perhaps no more or less than this quality of thisness, or itselfness. It is this thisness that number disperses, flattening it out into equivalence. Number gives control, because number requires and supplies distinctness, the possibility of series and finitude (distinguishability and countability). But it does so at the cost of the sense of what is called the qualitative, which is to say the drastically asymmetrical, nonreversible world in which my meaning and value is never commutable into yours or hers. This absolute equivalence is what we may as well call death: death, not as an absolute nonbeing, but as absolute equivalence, the absence of any noncommutable difference between one mode of being and another.

Number is always holding its own numerousness at bay. Numerals fight against the numerous, numbering being an attempt to steady and segment the dizzy delirium of one-after-another, or the one-beside-another, the one-and-then-another-one-just- like-it. It is not one’s death that is unique, own’s own-most, in Heidegger’s terms, but one’s being-towards-death, or dying into death. Death ‘itself’ is not the consummation of the singular, but the swallowing of the singular by the multiple, the process by which a unique person enters the general ‘one’ of ‘one dies’.

Alain Badiou has recently offered us a Platonic account of number, number as ontology, in answer to the Bad Infinity of modern numbers, for which he has bottomless contempt – voting, markets, statistics, ‘the ideological socialisation of number’ (Badiou 2008, 9) , that gritty, churning porridge. His notion of the event seems as though it is the opposite of a Platonic conception, precisely because it is represented as thrillingly open and unfinished, but the important thing about the event for Badiou is that it both calls for and allows for a fidelity that is absolute and unswerving. My notion of number as innumerable delirium, as that which will always threaten to lead us into losing count, is meant to suggest the unavailability of this redemption.

Perceval, John (1840). A Narrative of the Treatment Experienced By a Gentleman, During a State of Mental Derangement; Designed to Explain the Causes and the Nature of Insanity, and the Expose the Injudicious Conduct Pursued Towards Many Unfortunate Sufferers Under That Calamity. London: Effingham Wilson.

Rotman, Brian (1993). Ad Infinitum: The Ghost in Turing’s Machine: Taking God Out of Mathematics and Putting the Body Back In. Stanford: Stanford University Press.